Yes they should. it will be highly watched and by far more watched then any other the other inaugurations given all of the circumstances! Any why to get there name out is good!
I don't really understand this sentiment - the need to "get their name out there". We're talking about the Beach Boys, for goodness' sake. They're literally one of the most famous bands in the entire world (along with the Beatles and a few other groups). EVERYONE and their dog knows of the Beach Boys! Of course, probably 99% of people only know a couple of songs, but that's probably also the case with many other bands (I'd be willing to bet that a lot of people couldn't go beyond Satisfaction if asked to name Rolling Stones songs).
If Mike and Bruce played at the inauguration, they would undoubtedly play the biggest hits - California Girls, etc... They'd hardly be up there playing Vegetables or any other obscure track. In other words, if they play the inauguration it's unlikely to win them any new fans because everyone knows those songs already. I just can't see anyone turning on the TV, watching Mike mime his way through Kokomo and going "wow, I really need to check these "Beach Boys" out!" and running out to buy a copy of Holland.
Their name is already "out there" and playing the Trump inauguration is not going to increase the general public's awareness of the band. What it might do, as others have pointed out, is tarnish their reputation among existing fans.
I totally understand what you mean. But this 24-year-old at least knew of the BBs and surf music. It's a very shallow knowledge of the band, but at the end of the day it's still knowledge and awareness of the band's existence. I don't think it's just an age thing. I'm in my 40s and when I tell people I'm going to see Brian they assume it's going to be about the surfing songs - absolutely no awareness of the late 60s stuff and beyond. My mom, who is of the same age as the BBs, says that she likes them. But she only really knows their earlier stuff.
It's just the way it goes. The vast majority of people tend to be casual listeners/fans - regardless of the band. Few people feel compelled to really dig in the way those of us here do. It doesn't bother me in the slightest.